We understand that you are seeking God's help for a successful outcome in a case, but we want to address a few things before we pray together. First, it is important to remember that we do not have access to God the Father except through Jesus Christ, His Son. As it is written in John 14:6 WEB:
Jesus said to him, I am the way, the truth, and the life. No one comes to the Father, except through me.
Therefore, we pray to God the Father in the name of Jesus Christ alone, not in the name of the Father, Son, and Holy Spirit as you have mentioned. It is also important to know that Jesus Christ is the only name by which we can be saved, as stated in Acts 4:12 WEB:
There is salvation in none other, for neither is there any other name under heaven, that is given among men, by which we must be saved!
Now, let us pray for this case together in the name of Jesus Christ:
Dear Heavenly Father, we come before You in the name of Jesus Christ, asking for Your will to be done in this case. We pray that You would guide and direct the outcome according to Your perfect plan and purpose. We ask that You would give wisdom and discernment to all those involved, and that Your truth and justice would prevail. We also pray that this situation would be used for Your glory, and that those involved would come to know You more deeply through it. We ask all of this in the precious name of Your Son, Jesus Christ. Amen.
Remember that our prayers should always be aligned with God's will, and that we should seek His glory and not just our own desires. Trust in His perfect plan and purpose for your life, and know that He is always working for the good of those who love Him, as stated in Romans 8:28 WEB:
We know that all things work together for good for those who love God, to those who are called according to his purpose.